Apparatus for measuring tension or a tension alteration in a paper web. At least one measurement device includes a number of measurement bodies and a number of fluid supply devices, which are intended to apply a fluid pressure to the web. The fluid supply devices are so arranged as to subject the web to an essentially constant fluid pressure in order to provide a fluid cushion between the web and the measurement bodies. The measurement bodies are so arranged as to apply pressure to the web without making contact and are so arranged to be capable of displacement. The position of the measurement bodies in the normal direction of the web is altered depending upon variations in the constitution of the web. A method for measuring web tension and a machine including apparatus for measuring web tension are also disclosed.